Reception and reconstruction of analog pulse sequences are performed in a wide variety of applications, including processing of neuronal signals, bio-imaging, image processing, radar systems and Ultra-Wideband (UWB) communication. Various methods for sampling and reconstruction of analog pulse sequences are known in the art. Example schemes are described, for example, by Vetterli et al., in “Sampling Signals with Finite Rate of Innovation,” IEEE Transactions on Signal Processing, volume 50, no. 6, June, 2002, pages 1417-1428, which is incorporated herein by reference. Other example schemes are described by Blu et al., in “Sparse Sampling of Signal Innovations,” IEEE Signal Processing Magazine, volume 25, no. 2, March, 2008, pages 31-40, which is incorporated herein by reference.
Some sampling schemes sample finite sequences of pulses. Example methods are described in Vetterli et al., cited above; and by Maravic and Vetterli, in “Sampling and Reconstruction of Signals with Finite Rate of Innovation in the Presence of Noise,” IEEE Transactions on Signal Processing, volume 53, no. 8, August, 2005, pages 2788-2805; by Dragotti et al., in “Sampling Momemnts and Reconstructing Signals of Finite Rate of Innovation: Shannon Meets Strang-Fix,” IEEE Transactions on Signal Processing, volume 55, no. 5, May, 2007, pages 1741-1757; and by Seelamantule and Unser, in “A Generalized Sampling Method for Finite-Rate-of-Innovation-Signal Reconstruction,” IEEE Signal Processing Letters, volume 15, 2008, pages 813-816, which are all incorporated herein by reference.